Euler characters for general linear Lie superalgebra

M. Gorelik and Th. Heidersdors in the papers \cite{GH} investigated Euler characters for Lie superalgebra $\mathfrak{g}\mathfrak{l}(m,n)$ and $\mathfrak{o}\mathfrak{s}\mathfrak{p}(m.2n)$. In the present paper we also investigate Euler characters for Lie superalgebra $\mathfrak{g}\mathfrak{l}(m,n)$ but we use a different approach and our results are formulated in different terms.